Restricted volumes and divisorial Zariski decompositions

Details Restricted volumes and divisorial Zariski decompositions Restricted volumes and divisorial Zariski decompositions

2010-05-10

arxiv.org/abs/1005.1503v1

Mathematics

Algebraic Geometry

24 pages.

Scientific paper

We give a relation between the existence of a Zariski decomposition and the behavior of the restricted volumes of a big divisor on a smooth complex projective variety. Moreover we give the formula expressing a restricted volume with current integration by using analytic methods. This implies that we can define the restricted volume of a transcendental class on a compact K\"ahler manifold in natural way. The similar relation can be extended to a transcendental class.

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